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# Courses Offered in Math

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### FYMA 100: First Year Seminar (Mathematics)

This course will introduce student to the experience of academic exploration that is at the heart of a liberal arts education. Through study of one or more compelling questions or topics in a small seminar setting, students will practice creative and critical thinking and will learn to express themselves effectively and appropriately in a college setting. They will develop relationships and practices that allow them to effectively utilize college resources and become members of a community of learners. The specific topic of the seminar will be developed by individual faculty and will be announced in advance. First year seminars are required for first-year students and transfer students with fewer than 15 credits. Not open to students who have received credit for IDS189 or another first year seminar course.

Credits: 3.00

This course fulfills these general education curriculum requirements: First Year Seminar

### MAT 103: Mathematics for the Liberal Arts

This course is designed to give the liberal arts student, as well as other interested students, an introduction to some mathematical topics which broadly reflect the nature of the discipline. Topics are selected to highlight mathematical problem solving, the use of mathematical models and/or analysis of quantitative data. Topics may include probability and descriptive statistics, voting theory, graph theory, cryptography, game theory, chaos, and problems relating to the environment. Classroom lectures and discussions cover the basic theories. These are followed by writing assignments which form an essential component of the course. Not open to math majors without the permission of the Department Chairperson. Three lecture hours per week. This course satisfies the Quantitative Reasoning category. Not open to those students who received credit for MAT 120.

Prerequisite: Completion of the Basic College Mathematics Competency Requirement.

Credits: 3.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 123: (Formerly Mathematics for Elementary School Teachers I) Mathematics for the Childhood Education I

This course is the first in a sequence designed for prospective early childhood and elementary teachers. The course focuses on the PreK-8 vertical progression of content and skill development around number and operation. Mathematical topics include numeration systems, algorithms and estimation for the arithmetic operations, basic number theory, fractions and decimals, and patterns and sequences. Use of manipulatives and relevant technology may be integrated into the course. Three lecture hours per week.

Prerequisite: Satisfaction of the Basic Mathematics Competency requirement. Required for Early Childhood and Elementary Education Majors.

Credits: 3.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 124: (Formerly Mathematics for Elementary School Teachers Ii) Mathematics for Childhood Educators II

This course is the second in a sequence designed for prospective early childhood and elementary teachers. The course focuses on the PreK-8 vertical progression of content and skill development around geometry, measurement, statistics, and probability. Mathematics topics will include geometric figures and solids, congruence, similarity, constructions, measurement including perimeter, area, surface area and volume, geometric transformations, descriptive statistics and basic probability theory. Use of manipulatives and relevant technology may be integrated into the course. 3 lecture hours per week.

Prerequisites: Satisfaction of the Basic Mathematics Competency requirement. Required for Early Childhood and Elementary Education Majors.

Credits: 3.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 128: Quantitative Methods for Business and Finance

This course is an introduction to the mathematics used in business. Topics may include graphing linear equations and inequalities, solving systems of linear equations and inequalities, linear programming, simple and compound interest, annuities, descriptive statistics, and rates of change. Three lecture hours per week. Not open to student who have received credit for MAT 108.

Prerequisite: Satisfaction of the Basic Mathematics Competency Requirement.

Credits: 3.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 147: Statistics

This course is an introduction to elementary data analysis. Topics will include descriptive statistics. Normal distributions, sampling, interval estimation, testing of hypotheses, and linear regression. The emphasis is on practical and usable results, rather than on mathematical derivations. This course is intended to prepare students to use statistics in business, nursing, the social sciences, or education. Offered each semester. Three lecture hours per week. Prerequisite: Completion of the Basic College Mathematics Competency Requirement.

Credits: 3.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 150: Precalculus

This course is intended to prepare the student for the study of Calculus. Topics include: properties of the real number systems; absolute values, inequalities; detailed study of linear and quadratic equations; polynomial and rational functions and their graphs; exponential, logarithmic, and trigonometric functions. Three lecture hours per week. Not open to those students who received credit for MAT202N or MAT110.

Prerequisite: Completion of the Basic College Mathematics Competency Requirement.

Credits: 3.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 214A: Discrete Structures

A study of discrete mathematical structures of interest in computer science and other applied fields. Topics will be chosen from logic, proof techniques, sets, boolean algebra, functions, relations, basics of counting, recursion, graphs, trees, and discrete probability. Four lecture hours per week. Not open to students who have received credit for either MAT214 or MAT314.

Prerequisite: MAT220.

Credits: 4.00

### MAT 218: Introduction to Mathematical Computing

An introduction to a computer algebra system. Topics include the application of a computer algebra system to plotting functions, solving equations, simplifying expressions, and the creation of clear and attractive mathematical reports. One lecture hour per week.

Prerequisite: MAT220.

Credits: 1.00

### MAT 220: Calculus I

An introduction to the differential calculus of real-valued functions of one real variable. Topics include limits and derivatives and their applications in a context that includes polynomial, rational, trigonometric, exponential, and logarithmic functions. Offered each semester. Four lecture hours per week. Required of all Mathematics majors.

Prerequisites: Completion of the Basic College Mathematics Competency Requirement and either MAT110 or MAT150 or a thorough knowledge of trigonometric and logarithmic functions.

Credits: 4.00

This course fulfills these general education curriculum requirements: Quantitative Reasoning

### MAT 221: Calculus II

An introduction to the integral calculus of real-valued functions of one real variable. Topics include infinite sequences and series of real numbers and integrals and their applications in a context that includes polynomial, rational, trigonometric, exponential, and logarithmic functions. Offered each semester. Four lecture hours per week. Required of all mathematics majors.

Prerequisite: MAT220.

Credits: 4.00

### MAT 225: Mathematics for Childhood Educators III

This course is the third required math course for preservice early childhood and elementary teachers. The course focuses on the PreK-8 vertical progression of content and skill development around proportional reasoning and functions, through studying issues of social justice. Mathematical topics include problem solving, ratios and proportional reasoning, patterns and functions, and linear and exponential growth and decay. These topics will be explored in the context of social justice issues, such as: inequalities around race and identity; representation in elected office and voting rights; and inequities in economics, health, education, and climate. 3 lecture hours per week.

Prerequisites: MAT123, MAT124. Required for Early Childhood and Elementary Education Majors.

Credits: 3.00

### MAT 234: Introduction to Mathematical Proof

This course is an introduction to mathematical proof and the fundamental notions of higher mathematics. Topics include the basics of propositional logic, set theory, number theory, mathematical induction, functions, equivalence relations, and cardinality with an emphasis on writing proofs. Three lecture hours per week.

Prerequisites: MAT220 and a W-I course.

Credits: 3.00

This course fulfills these general education curriculum requirements: Written Communication-Level II

### MAT 240: Linear Algebra I

This course is an introduction to vector spaces and linear transformations primarily in Euclidean spaces. Topics include the algebra of matrices, linear independence, determinants, eigenvalues, and eigenvectors. Three lecture hours per week. Required of all mathematics majors.

Prerequisite: MAT220.

Credits: 3.00

### MAT 303A: Abstract Algebra I

This course is a proof-oriented introduction to groups. Topics will include examples and elementary properties of groups, subgroups, cyclic groups, symmetry groups, group isomorphisms and homomorphisms, normal subgroups and quotient groups, and direct products of groups. Three lecture hours per week. Not open to students who have received credit for MAT303.

Prerequisites: MAT234.

Credits: 3.00

### MAT 316: Combinatorial Mathematics

This course is a survey of combinatorial methods. Topics may include graphs, trees, networks, permutations and combinations, partitions, and enumeration theory. Three lecture hours per week.

Prerequisite: MAT234.

Credits: 3.00

### MAT 320: Calculus III

An introduction to two and three dimensional analytic geometry and an extension of the ideas of calculus to both real-valued functions of several variables and vector-valued functions. Topics include polar, cylindrical and spherical coordinates, vectors in two and three dimensions, limits, derivatives and integrals of functions of several variables and vector-valued functions. Offered each fall. Four lecture hours per week. Required of all mathematics majors.

Prerequisite: MAT221.

Credits: 4.00

### MAT 323: Numerical Analysis

A study of numerical methods. Topics include root finding for nonlinear equations, polynomial interpolation, series methods, numerical integration, finite differences, and solutions of linear systems. Efficiency, accuracy and round off and truncation errors are considered. Computer implementation of selected methods is included. Three lecture hours per week.

Prerequisite: MAT221.

Credits: 3.00

### MAT 403: Abstract Algebra II

Topics include normal subgroups, ideals, morphisms of groups and rings, fields and field extensions with examples and applications. Three lecture hours per week. Not open to students who have received credit for MAT404.

Prerequisite: MAT303A.

Credits: 3.00

### MAT 406: Modern Geometry

This course is a study of topics in advanced geometry from three perspectives: synthetic, analytic, and transformational. Topics include advanced results in Euclidean geometry, axiomatic development of Euclidean and non-Euclidean and non-Euclidean geometries, the use of coordinates, transformations, and symmetries. Writing, primarily in the form of mathematical proof, is an essential component of the course. Three lecture hours per week. Required of all Mathematics majors with a Secondary Education minor. Not open to students who have received credit for MAT405.

Prerequisite: MAT234 and MAT240..

Credits: 3.00

### MAT 407: Probability and Mathematical Statistics I

This course is an introduction to probability models and random variables. Topics may include simple counting methods, expectation, variance, moment and moment generating functions, the binomial, Poisson, exponential, and Normal distributions. Three lecture hours per week. Required of all Mathematics majors with a Secondary Education minor.

Prerequisite: MAT221

Credits: 3.00

### MAT 409: Complex Variables

This course is a study of functions of a complex variable. Topics may include Cauchy-Riemann equations, Cauchy's integral theorem and formula, the calculus of residues, series expansions of analytic functions, singularities, and contour integration. Three lecture hours per week.

Prerequisite: MAT221 and MAT234.

Credits: 3.00

### MAT 410: History of Mathematics

This course is a survey of the fundamental developments in mathematics from ancient to modern times, with special attention to the historical and logical bases of geometry, algebra, and analysis. Three lecture hours per week.

Prerequisite: MAT221.

Credits: 3.00

### MAT 411: Real Analysis

This course is a rigorous study of the fundamental ideas of calculus. Topics may include sequences, limits, continuity, derivatives, and integrals. Three lecture hours per week. Required of all mathematics majors.

Prerequisite: MAT221 and MAT234

Credits: 3.00

### MAT 413: Ordinary Differential Equations

This course is a study of the methods of solving linear and elementary nonlinear ordinary differential equations. Topics may include variation of parameters, series solutions, Laplace transforms and applications. Three lecture hours per week.

Prerequisite: MAT304A.

Credits: 3.00

### MAT 414: Linear Algebra II

This course is a continuation of Linear Algebra I. Topics include diagonalization, similarity, orthogonality, quadradic forms, inner products, and the singular value decomposition. Applications of these topics will be highlighted. Three lecture hours per week.

Prerequisite: MAT304A., MAT240

Credits: 3.00

### MAT 417: Probability and Mathematical Statistics II

This course is an introduction to statistical inference. Topics may include sampling distributions, limit theorems, point and interval estimation, hypothesis testing, linear regression and correlation, analysis of variance, and nonparametric methods. Three lecture hours per week. Prerequisite: MAT 407

Credits: 3.00

### MAT 420: Special Problems Seminar

This course is a study of field mathematics chosen by the instructor that is not covered in detail in other courses in the Mathematics Department. Topics chosen are determined by mathematical relevance and the perceived value that would be added to the mathematics curriculum.

Prerequisite: MAT221 and MAT234.

Credits: 3.00

### MAT 490: Senior Seminar in Mathematics

This course is a culminating experience for the mathematics major. Students will read mathematics journal articles, work problems and prove theorems derived from those articles, study topics independently, give oral presentations and write a mathematical paper. The paper may be expository or original in nature and students will hand in several drafts and make necessary revisions before the final product is completed. In the process, students will need to review and apply skills learned in previous courses as well as independently study new concepts. Students will be exposed to the "nuts and bolts" of doing mathematical research along the way, including using common databases for finding papers and typesetting a paper properly. Three lecture hours per week. Required of all mathematics majors.

Prerequisites: Successful completion of the calculus sequence (MAT220, MAT221 and MAT320) MAT240, a WII course; MAT411 or MAT303A.; and permission of the Mathematics Department Chairperson.

Credits: 3.00

This course fulfills these general education curriculum requirements: Written Commun-Level III

### MAT 500: Directed Study in Mathematics

The purpose of this course is to provide the student with an opportunity to explore in depth an area of mathematics that would not ordinarily be encountered in the program of required courses. It is recommended that the student take as many of the required courses as possible before enrolling in Directed Study. Credit for this course may not be applied toward Major requirements.

Prerequisites: At least one 400 level math course (with a grade of C or above), Junior or Senior standing, agreement of a Department faculty member to act as supervisor and permission of Mathematics Department Chairperson.

Credits: 3.00

### MAT 520: Mathematics Internship

An opportunity for students to gain practical or technical training in an industrial/commercial/research environment. The student makes the necessary arrangements with the chosen facility, in consultation with an appropriate faculty member. The internship must meet College Academic Policies (described elsewhere in this Catalog) and Mathematics Department Policy (available in the Mathematics Department). Open only to Junior/Senior Mathematics Majors who have obtained a faculty sponsor for this internship.

Prerequisites: Permission of a faculty supervisor and permission of the Department Chairperson.

Credits: 3.00 - 12.00

### MAT 701: Vector and Tensor Analysis

Suggested topics are: Definition of vectors and transformation equations, general Cartesian co-ordinates; vector and scalar products, geometry of space curves; introduction to differential forms and tensors.

Credits: 3.00

### MAT 702N: Research in Mathematics Education I

In this course, students will find and study current research on the teaching of mathematics at the middle and secondary levels. The course will examine concepts in research validity; data gathering; instrumentation selection and construction; validation and reliability determinations; sampling techniques; and research design. The course will review statistical models and techniques that are relevant to hypothesis testing in the context of mathematics education research problems. Three lecture hours per week. Open only to MAT and M.Ed. candidates for degree credit.

Prerequisites: A university-level course in statistics or permission from the M.A.T. Coordinator.

Credits: 3.00

### MAT 704: Linear Algebra

Topics include modules, linear dependence, matrix algebra, linear transformations, determinants, eigenvalues, linear systems, inner products, classical groups, diagonalization, symmetric matrices, function spaces, and differential operators.

Prerequisites: 6 hours of calculus and 3 hours of linear algebra.

Credits: 3.00

### MAT 705: Modern Plane Geometry

Suggested topics are: axiomatic approach to plane geometry, parallel postulate, Euclidean and hyperbolic geometries; quadratic extensions and angle trisection; plane measure.

Prerequisite: Two semesters of calculus.

Credits: 3.00

### MAT 706: Theory of Numbers

Suggested topics are: properties of divisibility, linear congruences; quadratic congruences; prime numbers, continued fractions; number-theoretic functions; primitive roots and quadratic residues.

Prerequisite: Permission of the Department Chairperson.

Credits: 3.00

### MAT 707: Mathematical Statistics

A calculus-based study of probability and statistics. Topics include probability models, discrete and continuous random variables and their distributions, bivariate and multivariate distributions, sampling distributions, limit theorems, point and interval estimation, theory and applications of hypothesis testing, linear regression and correlation.

Prerequisite: 12 hours of calculus.

Credits: 3.00

### MAT 708: Introduction to Cryptography

An introduction to cryptography - the study of methods of sending messages in disguised form, including some recent applications of number theory and group theory to public key cryptography. Topics include elementary number theory, finite fields, group theory, cryptosystems, and public key cryptography.

Prerequisite: Mathematical maturity as demonstrated by any one of the following - at least 12 credits of undergraduate or graduate math courses, or a score of 700 or higher on the math SAT or GRE.

Credits: 3.00

### MAT 709: Complex Variables

Complex numbers, analytic functions, derivatives and integrals of complex functions, Cauchy integral theorem and formula, Taylor and Laurent series, residues, maximum principles, conformal mapping, families of analytic functions and analytic continuation.

Prerequisite: Real Analysis I or the equivalent.

Credits: 3.00

### MAT 710: Foundations of Mathematics

Suggested topics are: propositional and predicate calculi, consistency and completeness of axiom systems, Godel's theorem, axiomatic set theory, cardinal and ordinal numbers.

Credits: 3.00

### MAT 711: Real Analysis I

Completeness, limits, continuity, convergence of sequences and series, derivatives, the Riemann integral, and theorems of Taylor, Bolzano-Weierstrass, and Heine-Borel together with applications.

Prerequisite: 12 hours of calculus or the equivalent.

Credits: 3.00

### MAT 713: Ordinary Differential Equations

Suggested topics are solutions of linear differential equations and systems of equations. Bessel and Legendre functions, Laplace transforms, series solutions, Sturm-Liouville theory, stability theory and singular points.

Prerequisites: 9 hours of calculus.

Credits: 3.00

### MAT 725: Fractal Geometry

A study of the geometry of fractal sets, self-similarity and fractal dimension. Suggested topics are: Iteration using the computer, graphical analysis, the Julia and Mandelbrot sets, chaos and applications to image compression, to dynamical systems and to computing the limiting perimeter and area enclosed by fractal sets.

Prerequisite: Acceptance into either the Master of Science in Mathematics, Master of Arts in Teaching Mathematics or the Master of Science in Geo-Information Science program or permission of the Mathematics Graduate program Coordinator.

Credits: 3.00

### MAT 731: Measure and Integration

Suggested topics are, metric spaces, topological spaces, abstract measure, outer measure, absolute continuity, measure spaces, measurable functions, Lebesgue-Stieltjes integration, product measure, Caratheodory outer measure, L-spaces, the Radon-Nikodym theorem.

Prerequisite: Real Analysis I or the equivalent.

Credits: 3.00

### MAT 734: Linear and Multilinear Algebra

Suggested topics are: canonical forms for matrices and linear transformations, quadratic forms, principal axis theorem, tensor products, exterior and symmetric algebras.

Prerequisite: Linear Algebra.

Credits: 3.00

### MAT 740: Computer Applications in Mathematics I

A programming language will be introduced and used to illustrate computer methods in Calculus, Number Theory, Linear Algebra, Statistics or Differential Equations. Attention is paid to machine accuracy, error estimation and multiple-precision arithmetic. Assignments include the coding and running of programs in the Math Lab or on a student’s personal computer. No previous computer experience required. Three lecture hours per week.

Credits: 3.00

### MAT 747: Applied Statistical Inference

A study of probability and statistical inference. Suggested topics are: Probability, discrete and continuous probability distributions, sampling distribution theory, confidence intervals, tests of statistical hypotheses, linear regression, and a nonparametric method: the Kolmogorov-Smirnov Goodness-of-Fit Test; applications to spatial statistics. The emphasis of the course is on applications and conceptual understanding, rather than on mathematical derivations.

Prerequisites: Acceptance into either the Master of Science in Mathematics, Master of Arts in Teaching Mathematics or the Master of Science in Geo-Information Science program or permission of the Mathematics Graduate Program Coordinator.

Credits: 3.00

### MAT 750: History of Mathematics

A survey course designed to deepen the student's knowledge of the vast literature of mathematics. Historically influential concepts will be examined for their effects on mathematics and the culture in which they evolved. Philosophical and psychological comparisons will be made between the mathematical and scientific developments in Ancient Greek times, in the Renaissance and Newtonian times, and in the 19th and 20th centuries.

Prerequisites: 9 hours of Calculus.

Credits: 3.00

### MAT 807: Statistical Inference

A continuation of MAT707. Suggested topics are multiple regression, analysis of variance, decision functions, Bayes solutions, and nonparametric methods.

Prerequisite: Mathematical Statistics.

Credits: 3.00

### MAT 90: Basic Algebra

This course is intended to develop those ideas, computational techniques, and methods of reasoning used in college mathematics, with an emphasis on algebra needed to formulate and solve first and second degree equations, constructing models using linear and quadratic functions, and concepts of coordinate geometry. Only for students entering Fall 1999 or later who have not passed either the Accuplacer Elementary Algebra Test or the College Level Math Test or for those students who entered before Fall 1999 who have not satisfied the Basic Mathematics Competency Requirement. Does not give degree credit. Three lecture hours per week.

Credits: 3.00

### MAT 910: Seminar in Mathematics

Intended primarily for graduate students seeking the degree of Master of Arts in Teaching Mathematics. The seminar will explore various topics in mathematics on an individual and group basis.

Credits: 3.00

### MAT 930: Seminar: Independent Study

Open only to students seeking the degree of Master of Science.

Credits: 3.00